<p><b>Abstract</b>—The <it>one-to-all broadcast</it> is the most primary collective communication pattern in a multicomputer network. We consider this problem in a wormhole-routed torus which uses the <it>all-port</it> and <it>dimension-ordered</it> routing model. We derive our routing algorithms based on the concept of “span of vector spaces” in linear algebra. For instance, in a 3D torus, the nodes receiving the broadcast message will be “spanned” from the source node to a line of nodes, to a plane of nodes, and then to a cube of nodes. Our results require at most <tmath>$2(k-1)$</tmath> steps more than the optimal number of steps for any square <tmath>$k$</tmath>-D torus. Existing results, as compared to ours, can only be applied to tori of very restricted dimensions or sizes and either rely on an undesirable non-dimension-ordered routing or require more numbers of steps.</p>